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Visually experience the beauty
of mathematics with p5.js
19 Nov, 2023 JSConf JP
@kkeeth @kuwahara_jsri @kkeeth
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Who am I
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4
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5
outputs
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npmjs.com/~kkeeth
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Let’s start 😆
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My Math History
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Undergraduate: Riemann's zeta function
(Part of Riemann hypothesis)
Graduate Student: Knot Theory
(Part of Volume conjecture)
My Math History
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A Million Dollars at Stake. Seven of the most
dif
f
icult problems in mathematics
One problem (the Poincaré Conjecture) was
solved (proved) by Perelman
Aside: “millennium prize problems”
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Introduction to
p5.js
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Do you know p5.js ? 😁
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URL: https://p5js.org/
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👉
About p5.js
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Processing
p5.js
Programming Language Java / (JavaScript) JavaScript
Operating Environment mainly PC Web Browser
Performance Normal little slow
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URL: https://editor.p5js.org/
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setup
This function is called once.
It's used to de
fi
ne initial
environment properties.
draw
Called directly after setup,
continuously executes the lines
of code contained inside its
block until the program is
stopped.
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setup
This function is called once.
It's used to de
fi
ne initial
environment properties.
draw
Called directly after setup,
continuously executes the lines
of code contained inside its
block until the program is
stopped.
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https://github.com/processing/p5.js/blob/v1.7.0/src/core/main.js#L418
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Experience the
beauty of
mathematics with
some p5.js examples
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Equation of a circle
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Equation of a circle
x2 + y2 = r2
O
θ
y
x
r
P(x, y)
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Equation of a circle
x2 + y2 = r2
O
θ
y
x
r
P(x, y)
x = ?
y = ?
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Polar Coordinate System
O
θ
r
x = r cos(θ)
y = r sin(θ)
(r ≥ 0)
P(r, θ)
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Trigonometric functions
(circular functions)
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URL: https://sites.google.com/site/cinderellajapan/huanocg/huano-qu-xian
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Quiz 💁
How does the following code behave?
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core part of this code
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Execution result
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Execution result
Fibonacci sequence
famous for sun
fl
ower seeds
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Fibonacci sequence
1, 1, 2, 3, 5, 8, 13, 21, 34...
1
1
,
2
1
,
3
2
,
5
3
,
8
5
,
13
8
,
21
13
,
34
21
. . .
1,2,1.5,1.66,1.6,1.625,1.615,...1.619... → 1.61803
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Fibonacci sequence
1, 1, 2, 3, 5, 8, 13, 21, 34...
1
1
,
2
1
,
3
2
,
5
3
,
8
5
,
13
8
,
21
13
,
34
21
. . .
1,2,1.5,1.66,1.6,1.625,1.615,...1.619... → 1.61803
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Fibonacci sequence
1, 1, 2, 3, 5, 8, 13, 21, 34...
1
1
,
2
1
,
3
2
,
5
3
,
8
5
,
13
8
,
21
13
,
34
21
. . .
1,2,1.5,1.66,1.6,1.625,1.615,...1.619... → 1.61803
Golden ratio
ϕ =
1 + 5
2
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Quiz 💁
What was used to draw
the next image?
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Lemniscate
orthogonal coordinate system
(x2 + y2)2 − 2a2(x2 − y2) = 0
polar coordinate system
r2 = 2a2 cos 2θ
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Lemniscate
x =
a cos(t)
1 + sin2(t)
y =
a sin(t)cos(t)
1 + sin2(t)
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Quiz 💁
What was used to draw
the next images?
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Euclidean Algorithm
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Euclidean Algorithm
a = bq + r (a ≥ b)
gcd(a, b) = gcd(b, r)
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Rose Curve
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r = sin(θ
n
d
)
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https://zenn.dev/kkeeth/articles/rose-curve-variations
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Flow FieldɾVector Field
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Ken Perlin’s
Perlin Noise
Pseudo Vector Field
Generation
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Digression
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🤔
Is there anything that combines
programming, mathematics and art ?
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✕ Mathematics
JavaScript Art works
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✕ Mathematics
JavaScript Art works
Creative Coding
Generative Art
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URL:https://www.pinterest.jp/pin/190980840435280107/ URL: https://www.pinterest.jp/pin/129267451795680561/
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URL: https://www.pinterest.jp/pin/353180795787592200/ URL: https://twitter.com/t_ritoco/status/1461470820274819072/photo/3
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Have fun with
p5.js 😆
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References
p5.js Get Started
• https://p5js.org/get-started/
δΣωϥςΟϒɾΞʔτɹProcessingʹΑΔ࣮ફΨΠυ
• https://www.amazon.co.jp/dp/4861009634
Pinterst Search(generativeart)
• https://onl.tw/2bhH4ZD
Openprocessing
• https://openprocessing.org/user/299354?o=13&view=sketches
𝕏
hash tag ”#ͭͿ͖Processing”
• https://x.com/search?q=ͭͿ͖Processing&src=typeahead_click&f=live
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